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Thread: Completing the square

  1. #1
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    Completing the square

    given that $\displaystyle (x+b)(x+a)=(x+2)^2-9$, find the value of a and b
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  2. #2
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    Quote Originally Posted by Punch View Post
    given that $\displaystyle (x+b)(x+a)=(x+2)^2-9$, find the value of a and b
    $\displaystyle x^2 + (a+b)x + ab = x^2 + 4x + 4 - 9$

    compare the coefficients of x^2, x and constant. Then solve for a and b.
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  3. #3
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    It's easier to factorise the RHS using DOTS

    $\displaystyle (x + 2)^2 - 9 = (x + 2)^2 - 3^2$

    $\displaystyle = (x + 2 + 3)(x + 2 - 3)$

    $\displaystyle = (x + 5)(x - 1)$.


    What do you think $\displaystyle a$ and $\displaystyle b$ are?
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